There is a soft cap maximum pressure at 3,000 psi in Section VIII-1, however speak with your AI and he will allow you to go above that soft cap.
In U-1 it states "(d) The rules of this Division have been formulated on
the basis of design principles and construction practices
applicable to vessels designed for pressures not exceeding
3,000 psi (20 MPa).[highlight #FCE94F]For pressures above 3,000 psi
(20 MPa), deviations from and additions to these rules
usually are necessary to meet the requirements of design
principles and construction practices for these higher
pressures.[/highlight] Only in the event that after having applied
these additional design principles and construction practices
the vessel still complies with all of the requirements
of this Division may it be stamped with the applicable Certification
Mark with the Designator."
It my case, we built some 5k psi vessels but were required to have an engineering firm check the design using finite element analysis. Again, speak with your AI and he will give you the best course of action for you.